{"id":16,"date":"2018-11-10T17:17:31","date_gmt":"2018-11-11T01:17:31","guid":{"rendered":"https:\/\/hailstonesequence.wordpress.com\/?p=16"},"modified":"2021-03-15T22:40:46","modified_gmt":"2021-03-16T05:40:46","slug":"how-do-we-know-that-something-is-true","status":"publish","type":"post","link":"https:\/\/hailstonesequence.com\/index.php\/2018\/11\/10\/how-do-we-know-that-something-is-true\/","title":{"rendered":"How do we know that something is true?"},"content":{"rendered":"\n<p>I&#8217;m trying to frame\/structure my units with essential questions this year. I don&#8217;t really know how to use them meaningfully to add coherence to a unit, but I&#8217;m going to track one of my attempts here:<\/p>\n\n\n\n<p>In Geometry our essential question (at least for this unit&#8230;.perhaps for the year?) is: How can we know for certain that something is true?<\/p>\n\n\n\n<p>I don&#8217;t have a clear goal, but I suppose I&#8217;m mainly trying to provide some context for the need for\/tradition of formal proofs. Middle schoolers are often deep in the throes of existential crises, anyway&#8230;.why not enrich math class with the occasional epistemological debate?<\/p>\n\n\n\n<p><strong>Day 1:<\/strong> To launch Unit 3: Reasoning and Proof, I explained that our guiding question for the unit was, &#8220;How do we know for sure that something is true?&#8221; and asked them to free write for a few minutes. I told them they could think about how it applied to math or think about it more generally.<\/p>\n\n\n\n<p>After a few minutes, they shared out, and I jotted down their ideas. It was a lot of fun, everyone was super engaged and math class felt MEANINGFUL.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/hailstonesequence.files.wordpress.com\/2018\/10\/screen-shot-2018-10-26-at-10-09-44-pm.png?w=723\" alt=\"Screen Shot 2018-10-26 at 10.09.44 PM\" class=\"wp-image-17\" data-recalc-dims=\"1\"\/><\/figure>\n\n\n\n<p>Afterwards, we talked about &#8220;inductive reasoning&#8221; and then used it to explore and make conjectures about vertical angles, linear pairs, and triangles. Some of the energy faded because the explorations felt obvious&#8230;sigh.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m trying to frame\/structure my units with essential questions this year. I don&#8217;t really know how to use them meaningfully to add coherence to a unit, but I&#8217;m going to track one of my attempts here: In Geometry our essential question (at least for this unit&#8230;.perhaps for the year?) is: How can we know for [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":805,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7,1],"tags":[30,37,57,64],"class_list":["post-16","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geometry","category-uncategorized","tag-essential-questions","tag-geometry-essential-questions","tag-proofs","tag-reasoning-and-proof"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2021\/03\/screen-shot-2018-10-26-at-10-09-44-pm.png?fit=1514%2C1126&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/16","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":1,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/16\/revisions"}],"predecessor-version":[{"id":968,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/16\/revisions\/968"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/media\/805"}],"wp:attachment":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/media?parent=16"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/categories?post=16"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/tags?post=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}